Sometime back, while reading Fazlollah M. Reza’s “An Introduction to Information Theory“, I revisited a solution that I have sketched out years back on the Eddington’s controvery problem. This problem is interesting to me because it exemplifies the type of confusion that existed in probability prior to the introduction of set theory considerations. Eddington is the same astrophysicist who did the solar eclipse experiment to demonstrate the prediction of light bending using Einstein’s general relativity. I thought I should share the solution which I co-solved with Yen Lee, an old friend from Cambridge who’s now a postdoc in Purdue University. To quote the problem, “If A, B, C, D each speaks the truth 1 in 3 times (independently), and A affirms that B denies that C delcares that D is a liar, what’s the probability that D was speaking the truth?” Historically, this problem was examined by M. Gardner in an article entitled “Brain Teasers that involve Formal Logic” and to everyone’s surprise, some theoretical physicists and mathematicians are embroiled in getting the correct the number of the solution. So, I will discuss the problem in detail, giving my solution to the problem and explain why Eddington’s answer of 25/71 was greeted with so much protests from the thinkers of the time. (Warning: If you are not a theoretical physicist or mathematician, you will be inundated by a plethora of mathematical symbols, hence you are warned before proceeding to the interesting parts). Continue reading A Mathematical Solution to Eddington’s Controversy Problem
Recently, while flipping through a research paper made me think about the estimation of π (which we know is 3.141… ). Here is an interesting problem which is associated with a method to estimate π. A needle of length a is thrown on to the plane covered with equally spaced parallel lines with seperation b. What is the probability that the needle will cross a line? How can this be extended to a random curve of length A? I thought I might just share a simple mathematical solution for both the Buffon’s Needle and Buffon’s Noodle problem that I have worked out years back on this problem during my PhD years.
Three days ago, I discovered that one of my colleagues from Singapore Angle shares the same birthday with me. It reminded me of this interesting first year Cambridge undergraduate mathematical problem: What is the least number of persons required if the probability exceeds 0.5 that two or more persons have the same birthday (excluding the year)? So, I will offer the solution to the birthday problem (on my birthday, of course) and examine some interesting implications about the solution to this problem. Continue reading The Birthday Problem